Open Access
·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X
Powered by:
The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to:
Random dynamical systems
Geometry and physics
Dynamical systems with hyperbolic behaviour
Real and complex geometry
Ergodic theory
Distance geometry
Topological dynamics
Global differential geometry
Infinite-dimensional Hamiltonian systems
Symplectic geometry, contact geometry
The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.
Issues up to 2022 co-published with and available at:
On the Irregular Part of V -Statistics Multifractal Spectra for Systems with Non-Uniform Specification
ALEJANDRO MESÓNMESON@IFLYSIB.UNLP.EDU.ARInstituto De Física De Líquidos Y Sistemas Biológicos (IFLYSIB) Conicet–UNLP and Grupo De Aplicaciones Matemáticas Y EstadísticasDe La Facultad De Ingeniería (GAMEFI) UNLP E-mails: ;INSTITUTO DE FÍSICA DE LÍQUIDOS Y SISTEMAS BIOLÓGICOS (IFLYSIB) CONICET–UNLP AND GRUPO DE APLICACIONES MATEMÁTICAS Y ESTADÍSTICAS DE LA FACULTAD DE INGENIERÍA (GAMEFI) UNLP, LA PLATA, ARGENTINALa Plata, ArgentinaView full profile →
, FERNANDO VERICATVERICAT.FERNANDO@GMAIL.COMInstituto De Física De Líquidos Y Sistemas Biológicos (IFLYSIB) Conicet–UNLP and Grupo De Aplicaciones Matemáticas Y EstadísticasDe La Facultad De Ingeniería (GAMEFI) UNLP E-mails: ;INSTITUTO DE FÍSICA DE LÍQUIDOS Y SISTEMAS BIOLÓGICOS (IFLYSIB) CONICET–UNLP AND GRUPO DE APLICACIONES MATEMÁTICAS Y ESTADÍSTICAS DE LA FACULTAD DE INGENIERÍA (GAMEFI) UNLP, LA PLATA, ARGENTINALa Plata, ArgentinaView full profile →
* Corresponding author · click or hover a name for details
Let (X, f) be a dynamical system with X a compact metric space. Let Xundefined be the product of r-copies of X, r≥ 1, and Φ: Xundefined → R. The multifractal decomposition for V –statistics for Φ, f is defined as undefined.The set of points x ∊ X, for which the limit does not exist is called the irregular part, or historic set, of the spectrum. In this article we analyze the irregular part of the V -statistics for systems satisfying a weak form of the known Bowen specification property, called the non-uniform specification property. This concept was introduced by P. Varandas and allows to work in a nonuniformly hyperbolic context.
References
V.Bergelson, Weakly mixing PET , Ergod. Th. and Dynam. Sys ., Vol. 7 , 337 – 349 ( 1987 ). J.Bourgain, Double recurrence and almost sure convergence , J. Reine Angew Math , Vol. 404 , 140 – 161 ( 1990 ). R.Bowen, Topological entropy for non-compact sets , Trans. Amer. Math. Soc ., Vol. 184 , 125 – 136 ( 1973 ). X.Zhou and E.Chen, Multifractal analysis of ergodic averages in some nonuniformly hyperbolic systems , preprint, arXiv:1310.2348v1 ( 2013 ). A. H.Fan, J.Schmeling and J.Wu, The multifractal spectrta of V –statistics , preprint, arXiv:1206.3214v1 ( 2012 ) A.Fan, D. J.Feng and J.Wu, Recurrence, dimension and entropy , J. London Math. Soc ., Vol. 64 , 229 – 244 ( 2001 ). A.Fan, I. M.Liao and J.Peyrière, Generic points in systems of specification and Banach valued Birkhoff averages , Disc. Cont. Dynam. Sys ., Vol. 21 , 1103 – 1128 ( 2008 ). H.Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szmerédi on arithmetic progressions , J. d′ Analyse Math ., Vol. 31 , 204 – 256 ( 1977 ). A.Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms , Inst. Hautes Studes Sci, Publ. Math , Vol. 51 , 137 – 173 ( 1980 ). A.Meson and F.Vericat, On The topological entropy of the irregular part of V-statitistics multifractal spectra , Journal of Dynamical Systems and Geometric Theories , Vol. 11 1 – 12 ( 2012 ). C. E.Pfister and W.G.Sullivan, On the topological entropy of saturated sets , Ergod. Th. and Dynam. Sys ., Vol. 27 , 1 – 29 ( 2007 ). F.Takens and E.Verbitski, On the variational principle for the topological entropy of certain non-compact sets , Ergod. Th. and Dynam. Sys ., Vol. 23 , 317 – 348 ( 2003 ). D.Thompson, The irregular set for maps with the specification property has full topological pressure , Dynam Sys: An International Journal , Vol. 25 25 – 51 ( 2010 ). P.Varandas, Non-uniform specification and large deviations for weaks Gibbs measures , J. Stat. Phys ., Vol. 146 , 330 – 358 ( 2012 ). Z.Yin. E.Chen and X.Zhou, The historic set of ergodic averages in some non-uniformly hyperbolic systems , preprint, arXiv:1405.3339v1 ( 2014 ) L. S.Young, Large deviations in dynamical systems , Trans. Amer. Math. Soc ., Vol. 318 , 525 – 543 ( 1990 ). P.Walters, An introduction to Ergodic Theory , Springer-Verlag , 1982 .
Views: 5Downloads: 7Citations: 1
Install Journal of Dynamical Systems and Geometric TheoriesFaster access from your home screen
